U.S. Pat. No. 4,408,700 (William E. Fillmore et al.) discloses a dispensing package which is made up of a container having an externally threaded finish portion with a closure threadably secured to such finish portion. The closure includes an axially shiftable or pop-up valve element which is movable with respect to the other structure of the closure between a closed, flow blocking, position and an open, flow permitting, position. The package of this reference does not incorporate tamper evident features, and such a package cannot be stored in an inverted position on its closure due to the fact that the top of the dispensing valve element extends beyond the surrounding structure of the closure, even in the closed position of the valve element. Further, a package of the type described in the aforesaid U.S. Patent requires that a user use both hands in opening and closing the package in a normal fashion, one hand to grasp a container and the other hand to manipulate the valve element, due to the fact that the valve element can only be moved by the application of a force extending along its longitudinal axis.